Question

The Montgomery Park officials plan to construct a concession stand beside an access road. They will also construct asphalt pathways from the volleyball court and the tennis court to the concession stand. Describe how to determine where the concession stand should be to minimize the amount of asphalt needed. Include a diagram.

Answer 1

What course are you in as that will determine how I word my answer.

Answer 2

It is for Geometry

Answer 3

Okay, then this answer will be more qualitative than quantitative. The concession stand will be along the access road and in between the boundaries of 2 vertical lines drawn straight down from the 2 points on the drawing. You are not given distances so we can only speak in generalities, but the general method for the location of the concession stand is determined by putting this diagram on a coordinate system and getting the distance from the concession stand and the 2 points in terms of (x, y) coordinates. The distances will be determined by the Pythagorean theorem. If you had actual locations for the dots, then the minimal distance can be gotten easily using differential calculus.

Answer 4

So I have to graph this then?

Answer 5

I don't think you are supposed to find the actual location, just describe how to go about it. But graph-wise, which I don't think you are required to do would be like this:

And you would have to get the measures of "a" and "b".

Answer 6

How do I get the measures of a and b?

Answer 7

Where I drew the dotted lines, you have 2 right triangles. The measures of those 2 legs can be known because the volleyball and tennis courts are already there, so those distances are readily available. The solid lines are the hypotenuses. And the distance on the access road from the one dotted line to the other is a given because, again, the volleyball and tennis court locations are already "known".

Answer 8

So, if the distance on the access road from one dotted line to the other is "d", then the point where the two solid angled lines meet break up "d" into "d1" and "d2". The key here is that you don't have to work with 2 unknown quantities (d1 and d2). You can work with just one unknown, d1, and the other length will be "d - d1" "d" is a "given" or "known" length.

Answer 9

I`m so confused...How do I put numbers into that though or figure it out

Answer 10

So, the total asphalt is the 2 solid lines which are hypotenuses and the legs are the 2 dotted lines and d1 and "d - d1". You can't put numbers in at this point because you have no actual measurements. But as long as we have the total distance given in just one independent variable, "d1", we could do this problem by this method. I don't think you are supposed to give a numerical answer. I think you are supposed to describe a method. I can give you a little more detail if this is not clear yet.

Answer 11

No that is fine. Thank you so much!

Answer 12

Are you sure? It is indeed all here, and if you re-read, you will get it I'm sure, but I would stick with you if you wanted.

Answer 13

In any case, good luck in all of your studies and thx for the recognition! @Brittanyy!

Answer 14

thanks and your welcome (:

Answer 15

Asphalt length = sqrt(x^2 + (d1)^2) + sqrt(y^2 + (d - d1)^2)

And x, y, and d are all known. Only one independent variable "d1".